Find The Answer To The Image Below, 15 POINTS

1. Using Newton's method, the only critical number of the function f(x) = ln(1 + x - x^2 + x^3) is approximately 0.789813.

2. The equation of the line passing through the point (3,5) that cuts off the least area from the first quadrant is y = -(5/3)x + 20/3.

3. The function f(x) = sin(x^2) - 137x + 231 is the function that passes through the point (137, 0) and has a derivative function of f'(x) = 12x cos(x^2).

To find the critical number of the function f(x) = ln(1 + x - x^2 + x^3), we can apply Newton's method.

The derivative of f(x) is given by f'(x) = (1 - 2x + 3x^2) / (1 + x - x^2 + x^3). By iteratively applying Newton's method with an initial guess, we can approximate the critical number. The process continues until we reach the desired level of accuracy. In this case, the critical number is approximately 0.789813.

To find the line passing through the point (3,5) that cuts off the least area from the first quadrant, we need to minimize the area of the triangle formed by the line, the x-axis, and the y-axis.

The equation of a line passing through (3,5) can be written as y = mx + c, where m represents the slope and c is the y-intercept. By minimizing the area of the triangle, we minimize the product of the base and height.

This occurs when the line is perpendicular to the x-axis, resulting in the least area. Therefore, the line equation is y = -(5/3)x + 20/3.

To find the function f(x) that passes through the point (137, 0) and has a derivative function of f'(x) = 12x cos(x^2), we integrate the derivative function with respect to x.

Integrating f'(x) gives us f(x) = sin(x^2) - 137x + C, where C is the constant of integration. To determine the value of C, we substitute the given point (137, 0) into the equation. This gives us 0 = sin(137^2) - 137(137) + C, which allows us to solve for C. The resulting function is f(x) = sin(x^2) - 137x + 231.

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Answer:

4.8

Step-by-step explanation:

Not sure if this is what you're asking but because it is equilateral each side is the same. So you divide 14.4 by 3, to get 4.8.

In order to calculate the total number of employees, we can use the following rule of three:

Now, from this rule of three, we can write the following proportion and solve it for x:

Rounding to the nearest whole number, the total number of employees is 65741.

The linear equation that passes through the points (2, -2) and (0, -1) is y = -1/2x - 1.

The two points are (2, −2) and (0, −1), we will use the point-slope form to write the equation of a line through these points.

Point-slope form of a linear equation is given asy − y1 = m(x − x1)

where (x1, y1) is any point on the line and m is the slope of the line.

Let us find the slope of the line through the given two points.

The slope m is given asm = (y2 − y1) / (x2 − x1)

Substituting the given values, we getm = (-1 - (-2)) / (0 - 2) = 1 / 2

So, the slope of the line is 1 / 2.

Using the coordinates of the given points (2, -2) and (0, -1):

m = (-1 - (-2)) / (0 - 2)

= (1) / (-2)

= -1/2

Now that we have the slope, let it be one of the points You can find the y-intercept (b) by substituting in the slope-intercept form with Let's use point (2, -2):

-2 = (-1/2)(2) + b

Simplification:

-2 = -1 + b

add 1 to both sides

-2 + 1 = b

b = -1

Now that we know the slope (m = -1/2) and the y-intercept (b = -1) we can write the equation .

y = -1/2x - 1

Let us choose the point (2, −2) to write the equation of the line.

y − y1 = m(x − x1)y − (−2)

= (1 / 2)(x − 2)y + 2

= (1 / 2)x − 1y

= (1 / 2)x − 3

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The equation of the line that passes through point (2, - 2) and (0, - 1) is equal to y = (- 1 / 2) · x - 1.

In this question we must derive the equation of a line that passes through points (2, - 2) and (0, - 1). Lines are defined by equations of the form:

y = m · x + b

m = Δy / Δ x

Where:

First, determine the slope of the line:

m = [- 1 - (- 2)] / (0 - 2)

m = - 1 / 2

Second, find the intercept:

b = y - m · x

b = - 1 - (- 1 / 2) · 0

b = - 1

Third, write the resulting equation of the line:

y = (- 1 / 2) · x - 1

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Answer:

The given line of best fit is: T = 6.5d + 11.8

We can use this equation to estimate the total burn time for a candle with a diameter of 0.5 inches:

T = 6.5(0.5) + 11.8

T = 3.25 + 11.8

T = 15.05

So, according to the line of best fit, the total burn time of a candle with a diameter of 0.5 inch would be approximately 15.05 hours.

Therefore, the answer is D. 15 hours.

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We have the following:

<1 and <6 are supplementary angles, that is, the sum of these two is equal to 180 degrees

replacing:

The answer is D. (179 -4x)°

Answer:

The anwser is 10

Step-by-step explanation:

Its not very hard just hold up 8 fingers then add 2 more

im and very sorry if i didn't understand the question its my first time using this app

Answer:

v=-3

Step-by-step explanation:

Isolate the variable by dividing each side by the factor that does not contain the variable.

Answer:

-3=V

Step-by-step explanation:

-301 - 5 = 6v -9(5-9v)

Distributive property on -9(5-9v

-301 - 5 = 6v -45 + 81v

add like terms together

-306 = 87v -45

add 45 on both sides

-261 = 87v

divide 87 on both sides

-3 = v

Hope this helps!

Answer:

8 pizzas

Step-by-step explanation:

If each of the 20 people eats 3/8 of pizza, to calculate the total number of pizzas needed, multiply 20 by 3/8 and round up to the nearest whole number.

\(\sf total \ number \ of \ pizzas=20 \times\dfrac38\)

                                  \(=\dfrac{20 \times3}8\)

                                  \(=\dfrac{60}8\)

                                  \(=\dfrac{15}2\)

                                  \(=7.5\)

Therefore, he should buy 8 pizzas for the party.

The value of the algebraic expression 11.5x + 10.9y  at x = 6 and y = 7 is 145.3

What is an algebraic expression?

Algebraic expression consists of variables and numbers connected with addition, subtraction, multiplication and division

The given algebraic expression is 11.5x + 10.9y

We have to find the value of the algebraic expression at x = 6 and y = 7

Putting x = 6 and y = 7 in the algebraic expression,

\(11.5 \times 6 + 10.9 \times 7\)

69 + 76.3

145.3

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9514 1404 393

Answer:

  B, C

Step-by-step explanation:

The sums are ...

  A) 59.45

  B) 118.16

  C) 18.97

  D) 27.76

Sums B and C have 8 in the ones place.

__

You can add the ones-place digits. If the resulting ones-digit is 7 or 8, then add the tenths-place digits. If the carry from that sum, added to the sum of ones-place digits, gives a value of 8 or 18, then you found a sum with a ones digit of 8.

Answer:

what do you mean oh woo oh when you nod your head yes but you want to say no what do you mean

Step-by-step explanation:

Answer:

the answer is x = 1

Step-by-step explanation:

delta math assignassignment

The solution is found by slope of the graph and the solution is 2,200.

Let x the amount of money per hour and y the total amount of money.

Studio A:-

Rents for 100 dollars plus 50 dollars per hour.

\(y= 100 + 50x\)

So the slope is 50 and the y intercept is 100.

Studio B:-

rents for 50 dollars plus 75 dollars per hour.

\(y= 50 + 75x\)

So the slope is 75 and the y intercept is 50.

ThrTh solution is 2200 , see the gragraphph.

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Complete question:- You and your friends decide to rent some studio time to make a CD. Big Notes Studio rents for $100 plus $50 per hour. Great Sounds Studio rents for $50 plus $75 per hour. Solve the system by graphic method.

The hypotheses for the test are H₀: σ₁² = σ₂² and H₁: σ₁² ≠ σ₂². This is a two-tailed test to assess if there is a difference in the standard deviations of sound levels between the areas designated as "casualty doors" and operating theaters. The claim being investigated is whether or not there is a difference in the standard deviations.

The hypotheses for the test are:

H₀: σ₁² = σ₂² (There is no difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

H₁: σ₁² ≠ σ₂² (There is a difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

This hypothesis test is a two-tailed test because the alternative hypothesis is not specifying a direction of difference.

To substantiate the claim that there is a difference in the standard deviations, we will conduct a two-sample F-test at a significance level of 0.10, comparing the variances of the two groups.

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The sum $a b c$ is 11760 if the ratio of the areas of two squares is  \($\frac{32}{63}$\).

Let the side length of the first square be x and the side length of the second square be y. Then we have:

\(\frac{Area of first square}{Area of second square} = \frac{x^2}{y^2} = \frac{32}{63}\)

By cross multiplying, we get:

63 x² = 32 y²

And then by rearranging:

\(\frac{x}{y} = \frac{4\sqrt{7} }{9}\)

Now, rationalizing the denominator, we get:

\(\frac{x}{y} = \frac{4\sqrt{7} }{9} . \frac{\sqrt{7} }{\sqrt{7} } = \frac{28\sqrt{7} }{63}\)

Thus, a.b.c = 28.7.63 = 11760.

Therefore, the value of the sum $a b c$ is 11760.

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From the given diagram, we can identify two right-angled triangles. The triangles are shown below:

Using trigonometric ratios, we can find x as follows

We can equate the expressions for DF as follows:

Solving for x:

Answer:

x = 5

A mathematical quantity having both direction and magnitude is called a vector.

A vector is a mathematical quantity that has both direction and magnitude. It is often represented graphically as an arrow, where the length of the arrow corresponds to the magnitude of the vector, and the direction of the arrow represents the direction of the vector.

Vectors are used in many areas of mathematics and science, including physics, engineering, and computer science. Some common operations performed on vectors include addition, subtraction, dot product, and cross product.

Vectors can also be expressed in various coordinate systems, such as Cartesian, polar, and spherical coordinates, depending on the context and application.

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The least amount of fencing required to enclose a rectangular pasture of 320,000 square meters is 600 meters by 533.3 meters. This is because the length of the sides is determined by the formula a=\(320,000\)b, where a is the area of the pasture and b is the length of the sides.

By solving for b, we get b=320,000a, and so a=600 and b=533.3.

Therefore, the dimensions of the pasture require 600 meters of fencing along one side, and 533.3 meters along the other side. No fencing is required along the river.

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Answer: -m*(x-3y)*(3x-y)

(*=multiply btw)

Step-by-step explanation:

STEP 1:

Equation at the end of step 1

 (m • ((x + y)2)) -  4m • (x - y)2

STEP2:

Equation at the end of step 2

 m • (x + y)2 -  4m • (x - y)2

STEP3:

3.1     Evaluate :  (x+y)2   =    x2+2xy+y2

3.2     Evaluate :  (x-y)2   =    x2-2xy+y2

STEP4:

Pulling out like terms

4.1     Pull out like factors :

  -3mx2 + 10mxy - 3my2  =   -m • (3x2 - 10xy + 3y2)

Trying to factor a multi variable polynomial :

4.2    Factoring    3x2 - 10xy + 3y2

Try to factor this multi-variable trinomial using trial and error

Found a factorization  :  (x - 3y)•(3x - y)

The simplified expression is given by (x² - 3x - 3) / ((x + 3)(x - 2)(x - 4)).

To simplify this expression, we need to find a common denominator for the two fractions and then combine them. To do this, we need to factor the denominators of both fractions.

Let's start with the first fraction's denominator:

x² + x - 6

We need to find two numbers that multiply to -6 and add to +1. These numbers are +3 and -2. Therefore, we can write:

x² + x - 6 = (x + 3)(x - 2)

Now let's factor the second fraction's denominator:

x² - 6x + 8

We need to find two numbers that multiply to 8 and add to -6. These numbers are -2 and -4. Therefore, we can write:

x² - 6x + 8 = (x - 2)(x - 4)

Now we can rewrite the original expression with a common denominator:

(x(x - 2) - (1)(x + 3)) / ((x + 3)(x - 2)(x - 4))

Next, we can simplify the numerator:

(x² - 2x - x - 3) / ((x + 3)(x - 2)(x - 4))

(x² - 3x - 3) / ((x + 3)(x - 2)(x - 4))

Finally, we can't simplify this expression any further. Therefore, the simplified expression is:

(x² - 3x - 3) / ((x + 3)(x - 2)(x - 4))

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Answer:

20 degrees

Step-by-step explanation:

every triangle had 3 angles that all add up to 180

the problem gives you two angles which are 120+40 which is 160

180-160 is 20 degrees which is whi it is the answer

Answer:

#1. 100
#2. 120

The inequality is 105 < x < 110, and the yeast will proof in temperatures that are at least 105°F and at most 110°F degrees.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have:

The ideal temperature for proofing yeast for baking is 107.5°F. However, yeast will proof within a variation of 2.5°F

Let x be the absolute value:

Then,

107.5 - 2.5 < x < 107.5 + 2.5

105 < x < 110

The Yeast will proof in temperatures that are at least 105°F and at most 110°F degrees.

Thus, the inequality is 105 < x < 110, and the yeast will proof in temperatures that are at least 105°F and at most 110°F degrees.

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Answer:D

Step-by-step explanation:

The critical value (t₍₃₀,₀.₀₅₎) for a 95% confidence interval, based on a random sample of 30 observations, is t₍₃₀,₀.₀₅₎ = 2.042.

To determine the critical value, we refer to the t-table with degrees of freedom (df) equal to n - 1, where n represents the sample size. In this case, the sample size is 30, so the degrees of freedom is 30 - 1 = 29.

For a 95% confidence interval, we need to consider the two-tailed critical region. Since the area in each tail is 0.025 (0.05/2), we look for the corresponding value in the t-table at a significance level of α/2 = 0.025 for df = 29.

The closest value to 0.025 in the table is 2.042.

Therefore, the critical value (t₍₃₀,₀.₀₅₎) for a 95% confidence interval based on a random sample of 30 observations is t₍₃₀,₀.₀₅₎ = 2.042.

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The Bootstrap Method is straightforward and straightforward to comprehend. First, it chooses randomly from the original sample to produce bootstrap samples from our initial sample.

After that, it uses summary statistics like variation, standard deviation, mean, and so on to get replicates, which is how we can calculate a confidence interval from that sample.

Thus, the answer is "Yes."

The bootstrap method is a resampling method that uses replacement sampling to estimate population statistics. It can be used to estimate standard deviation and mean summaries.

Remember that bootstrapping isn't only valuable for computing standard blunders, it can likewise be utilized to build certainty spans and perform speculation testing. When working with data that doesn't seem to lend itself to conventional methods, always remember bootstrapping techniques.

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Full Question = We want to find a 95% confidence interval for the standard deviation of a large dataset, given a sample.

Can the bootstrap method be used?

Group of answer choices

yes

no

Answer:

16 key chains

Step-by-step explanation:

Given

\(f(x) = 0.85x + 3.99\) ---company A

\(g(x) = 1.10x\) --- company B

Required

Value of x when \(f(x) = g(x)\)

We have:

\(f(x) = g(x)\)

\(0.85x + 3.99 = 1.10x\)

Collect like terms

\(0.85x - 1.10x = -3.99\)

\(-0.25x = -3.99\)

Solve for x

\(x = \frac{-3.99}{-0.25}\)

\(x = 15.96\)

\(x= 16\) --- approximated

Answer:

A

Step-by-step explanation:

X before Y

Answer:

2,2,2,11,11

Step-by-step explanation:

968/2

484/2

242/2

121/11

11/11

The price per unit that will yield maximum revenue is $67.04.

In order to find the price per unit that will yield maximum revenue, we have to follow the below-given steps:

Step 1: The revenue function for x units of a product is

R(x) = x * P(x),

where P(x) is the price per unit of the product.

Step 2: The demand function is

D(x) = 170e^(-0.04x)

Step 3: We are given that the 0 ≤ x ≤ 55, it means that we only need to consider this domain. Also, the price per unit of the product is unknown. Let's take it as P(x). Hence, the revenue function will be:

R(x) = P(x) * xR(x) = x * P(x)

Step 4: We need to find the price per unit that will yield maximum revenue. In order to do that, we have to differentiate the revenue function with respect to x and find its critical point. Let's differentiate the revenue function.

R'(x) = P(x) + x * P'(x)

Step 5: Now we will replace P(x) with D(x) / x from the demand function to obtain a function that depends on x only.

This will give us R(x) = x * (D(x) / x).

Simplifying this expression, we get R(x) = D(x).

Let's write it. R(x) = D(x)R'(x) = D'(x)

Step 6: Differentiate D(x) with respect to x, we get:

D'(x) = -6.8e^(-0.04x)

Step 7: To find the critical point of R(x), we will equate R'(x) to zero and solve for x.

R'(x) = 0D(x) + x * D'(x) = 0

Substitute D(x) and D'(x)D(x) + x * D'(x) = 170e^(-0.04x) - 6.8x * e^(-0.04x) = 0

Divide both sides by e^(-0.04x)x = 25

The critical point of R(x) is 25. It means that if the company sells 25 units of the product, then the company will receive maximum revenue.

Step 8: We need to find the price per unit that will yield maximum revenue. Let's substitute x = 25 in the demand function to find the price per unit of the product.

D(25) = 170e^(-0.04*25) = 67.04

Therefore, the price per unit that will yield maximum revenue is $67.04.

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